GMDH-Methodology and Implementation in C

The following sections are included:

• Preface
• Organization of the Chapters
• Intended Audience
• Resources for Readers
• About the Editor
• List of Contributors
• Contents

The group method of data handling (GMDH) [1] is a family of algorithms for computer-based mathematical modeling and structural identification. Most GMDH algorithms are characterized by an inductive self-organizing procedure used for obtaining a multiparametric model. Specific behavior characteristics of GMDH enabled its successful use in fields such as data mining, knowledge discovery, forecasting, complex systems modeling, optimization and pattern recognition…

This chapter presents the basic fundamentals of the GMDH multilayered iteration algorithm (MIA) network, which are well documented in the literature. The main steps for the computations of the GMDH algorithm are also presented. The functions are described as they appear in the accompanying CD, providing error-free computer code for this GMDH variant. Two examples are solved using the basic GMDH-MIA network: the first one, which is easier to model, is taken from Farlow's book [1], while the second one is taken from the author's laboratory experimental work on tool wear estimation. The results show that the basic GMDH-MIA network is useful for modeling; however, better results could be obtained by including some improvement strategies. Users can modify the code to meet their specific requirements and hence GMDH can become more useful to a wider range of the community involved in inductive modeling.

• Introduction
• Criterion Correction Algorithm
• C++ Implementation
  • Building sources
• Example
• Conclusion
• References

• The COMBI Algorithm
• Usage of the “Structure of Functions”
• Gradual Increase of Complexity
• Implementation
• Output Post-Processing
• Output Interpretation
• Predictive Model
• Summary
• References

This chapter presents a constructive approach to the group method of data handling (GMDH) polynomial harmonic functions. This is an approach to growing higher order networks, like those built by the multilayer GMDH algorithm, using activation polynomial harmonics obtained analytically from the data. Empirical results show that the polynomial harmonic version phGMDH outperforms the previous GMDH on time series modeling tasks.

• Modified Polynomial Neural Network
• Description of the Program of MPNN Calculation
  • The software framework (GMDH)
  • Object-oriented architecture of the software framework
  • Description of the program graphic interface
  • Description of the basic functions of the data processing interface
• The GMDH PNN Application in Solving the Problem of an Autonomous Mobile Robot (AMR) Control
  • The review of GMDH applications in robotics
  • The application of MPNN for controlling the autonomous mobile robot
• Application of MPNN for the Control of the Autonomous Cranberry Harvester
  • General project description
  • Formalization of the cranberry harvester control problem
  • Experiment results
• Conclusion
• References

This chapter presents the objective cluster analysis of data on the basis of the self-organization of clusterizations according to group method of data handling (GMDH) principles. New external criteria for the estimation of clustering quality (GMDH-criteria) are proposed. The GMDH-criteria are based on splitting of the initial sample X containing η clustered objects into two not intersecting equivalent subsamples A and B. Each subsample A for an object corresponds to a subsample B of the object. Together they form a pair named a dipole. The clustering for both subsamples A and B is carried out simultaneously; the sum of the intercluster distances for sample A, using the results of the clustering of sample B, and the same value for B using the results of the clustering of A, is calculated.

The GMDH-criteria generate a minimum area of underfitted clusterizations and allow the determination of the clusterization of optimal complexity in the case of noisy data.

• Introduction
• Honey Bee Swarm
• Clustering based on the Multiagent Approach
• Computer Code for Multiagent Clustering
  • Moving of agents
  • Natural selection
  • Evaluation of the conditions for objects in different cells
  • Main program: beeClustering
• Examples
  • Example 1: Synthetic data
  • Example 2: Real-world problem
• Conclusion
• References

This chapter presents the fundamentals of the basic analogue complexing inductive method, which are not well documented in the literature. The main goal of this chapter is an introduction to the analogue complexing inductive systems. Two main analogue complexing approaches are presented—a classical group method of data handling (GMDH) algorithm and a sophisticated task of long-range meteorological prognosis. The computer codes for classical analogue complexing and long-range meteorological prognosis methods are presented as examples. Users can modify the computer codes to meet their specific requirements and hence, the proposed codes can become more useful to a wider range of technical, economic, social, political and other data.

• Introduction
• Background of the GMDH-type Neural Network and Genetic Algorithm
• Description of the Genome Representation of the GMDH-GA Procedure
• GMDH-GA for Modeling the Tool wear Problem
• Stock Price Prediction Using the GMDH-type Neural Network
• Summary
• References

The following section is included:

• Index